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Solving a Quadratic Equation by Factorization Method

In the given ...

Question

In the given figure, $A C + A B = 5 A D$ and $A C - A D = 8$ Then find the area of the rectangle ABCD in sq.units?

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Solution

$G i v e n -$
$A B C D i s a r e c t a n g l e . A C + A B = 5 A D & A C - A D = 8 u n i t s .$
$T o o b t a i n - a r e a (A B C D) = ? .$
$S o l u t i o n - G i v e n t h a t A C + A B = 5 A D & A C - A D = 8 u n i t s .$
$S o e l i m i n a t i n g A C w e g e t A B = 4 A D - 8.$
$∴ a r . A B C D = A B \times A D = (4 A D - 8) \times A D .$
$(N o w w e c a n n o t p r o c e e d f u r t h a r a s w e n e e d t h e v l u e o f A D o r a n y s u i t a b l e d a t a t o d e t e r m i n e a r . A B C D .)$
$T h e a r e a c a n b e d e t e r m i n e d f o r a n y v a l u e o f A D, s a y 5. T h e n a r . A B C D = (4 A D - 8) \times A D = (4 \times 5 - 8) \times 5 s q . u n i t s = 60 s q . u n i t s .$
$I n t h a t c a s e A n s - a r . A B C D = 60 s q . u n i t s .$

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